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# Vampire Numbers!!

Topic closed. 5 replies. Last post 10 years ago by Maverick2842.

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Brazil
Member #49335
January 27, 2007
6 Posts
Offline
 Posted: February 28, 2007, 12:11 pm - IP Logged

Dear pick(3-4) hunters!!!

I know you are asking, "what the heck is a vampire number!?" I don't blame you, that's exactly what I thought when I bumped into them. Well, here's the story.... It all began when I happened to read the "Brain Bogglers" page in the June '95 issue of Discover magazine. I noticed that the author was Clifford Pickover, whom I knew from some of the fractal programs that I have of his, and from some of the wonderful books he has written. I usually don't bother with the Brain Boggler page, because I never have the patience to try and figure them out. But this one was different. Rather than try and explain it, here it is...

Brain Bogglers Interview With A Number by Clifford Pickover

If we are to believe best-selling novelist Anne Rice, vampires resemble humans in many respects but live secret lives hidden among mortals. There are also vampires in the world of mathematics, numbers that look like normal figures but bear a disguised difference. They are actually the products of two progenitor numbers that when multiplied survive, scrambled together, in the vampire number. Consider one such case: 27 x 81 = 2,187.

Another vampire number is 1,435, which is the product of 35 and 41. I define true vampires, such as the two previous examples, as meeting three rules. They have an even number of digits. Each one of the progenitor numbers has half the number of digits of the vampire. And finally, a true vampire number is not created simply by adding zeros to the ends of numbers, as in:
270,000 x 810,000 = 218,700,000,000.

True vampires would never be so obvious. Vampire numbers secretly inhabit our number system, but most have been undetected so far. When I grabbed my silver mirror and wooden stake and began my search for them, I found, in addition to the two listed above, five other four-digit vampire numbers. Can you find the others? Can you find any vampire numbers with more digits in them?

## All of the 4 digit TRUE vampires.

A number v = xy with an even number (n) of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y together is known as vampire number. Pairs of trailing zeros (Both the numbers have a trailing zero) are not allowed. If v is a vampire number then x and y are called its "fangs." Examples of 4-digit vampire numbers include

1. 21 x 60 = 1260
2. 15 x 93 = 1395
3. 35 x 41 = 1435
4. 30 x 51 = 1530
5. 21 x 87 = 1827
6. 27 x 81 = 2187
7. 80 x 86 = 6880

Vampire number counts
 Digits Vampireratio Vampires with at least f different fang pairs Vampireequations Primevampires f=1(all vampires) f=2 f=3 f=4 f=5 4 1/1286 7 0 0 0 0 7 0 6 1/6081 148 1 0 0 0 149 5 8 1/27881 3228 14 1 0 0 3243 57 10 1/82984 108454 172 0 0 0 108626 970 12 1/204980 4390670 2998 13 0 0 4393681 26653 14 1/431813 208423682 72630 140 3 1 208496456 923920

Vampire ratio is (n-digit vampire numbers)/(n-digit integers) and not a ratio of performed tests.
Vampire equations are all equations of the form vampire = fang1 · fang2, i.e. each vampire number counts for each different fang pair. Prime vampires obviously only have one fang pair.
The vampire equations for all table counts below 15 are on this page.

First 15 vampires with exactly 2 fang pairs
 125460 = 204 · 615 = 246 · 510 11930170 = 1301 · 9170 = 1310 · 9107 12054060 = 2004 · 6015 = 2406 · 5010 12417993 = 1317 · 9429 = 1347 · 9219 12600324 = 2031 · 6204 = 3102 · 4062 12827650 = 1826 · 7025 = 2075 · 6182 13002462 = 2031 · 6402 = 3201 · 4062 22569480 = 2649 · 8520 = 4260 · 5298 23287176 = 2673 · 8712 = 3267 · 7128 26198073 = 2673 · 9801 = 3267 · 8019 26373600 = 3600 · 7326 = 3663 · 7200 26839800 = 2886 · 9300 = 3900 · 6882 46847920 = 4760 · 9842 = 6290 · 7448 61360780 = 7130 · 8606 = 7613 · 8060 1001795850 = 10170 · 98505 = 19701 · 50850

"Then give to the world the best you have, And the best will come back to you."

United States
Member #17555
June 22, 2005
5582 Posts
Offline
 Posted: February 28, 2007, 12:23 pm - IP Logged

The first part was interesting, but I couldn't understand the Fang part.

I tell you..It was a pain in the neck trying to figuring it out...

United States
Member #17555
June 22, 2005
5582 Posts
Offline
 Posted: February 28, 2007, 8:04 pm - IP Logged

The first part was interesting, but I couldn't understand the Fang part.

I tell you..It was a pain in the neck trying to figuring it out...

I'm still trying....but it's hard for me to sink my teeth into it....Too tired!

I have no stake in this....Okay??...LOL

Wisconsin
United States
Member #1303
March 27, 2003
1508 Posts
Offline
 Posted: February 28, 2007, 9:32 pm - IP Logged

I tell you..It was a pain in the neck trying to figuring it out...

OW !  Now I'm afraid you must be destroyed.  Please follow the yellow lines on the floor which will take you to our disintegration chamber.......

============

How can you tell if a politician is lying?

United States
Member #17555
June 22, 2005
5582 Posts
Offline
 Posted: February 28, 2007, 9:42 pm - IP Logged

I tell you..It was a pain in the neck trying to figuring it out...

OW !  Now I'm afraid you must be destroyed.  Please follow the yellow lines on the floor which will take you to our disintegration chamber.......

This is starting to look like a Batman episode....

BLAM!........FOOM!........YIKES!

SLAM!...WHAP!

Robin: In the name of jehovian jumping jacks batman....!

Griffith, In
United States
Member #41637
June 20, 2006
266 Posts
Offline
 Posted: February 28, 2007, 9:54 pm - IP Logged

Dear pick(3-4) hunters!!!

I know you are asking, "what the heck is a vampire number!?" I don't blame you, that's exactly what I thought when I bumped into them. Well, here's the story.... It all began when I happened to read the "Brain Bogglers" page in the June '95 issue of Discover magazine. I noticed that the author was Clifford Pickover, whom I knew from some of the fractal programs that I have of his, and from some of the wonderful books he has written. I usually don't bother with the Brain Boggler page, because I never have the patience to try and figure them out. But this one was different. Rather than try and explain it, here it is...

Brain Bogglers Interview With A Number by Clifford Pickover

If we are to believe best-selling novelist Anne Rice, vampires resemble humans in many respects but live secret lives hidden among mortals. There are also vampires in the world of mathematics, numbers that look like normal figures but bear a disguised difference. They are actually the products of two progenitor numbers that when multiplied survive, scrambled together, in the vampire number. Consider one such case: 27 x 81 = 2,187.

Another vampire number is 1,435, which is the product of 35 and 41. I define true vampires, such as the two previous examples, as meeting three rules. They have an even number of digits. Each one of the progenitor numbers has half the number of digits of the vampire. And finally, a true vampire number is not created simply by adding zeros to the ends of numbers, as in:
270,000 x 810,000 = 218,700,000,000.

True vampires would never be so obvious. Vampire numbers secretly inhabit our number system, but most have been undetected so far. When I grabbed my silver mirror and wooden stake and began my search for them, I found, in addition to the two listed above, five other four-digit vampire numbers. Can you find the others? Can you find any vampire numbers with more digits in them?

## All of the 4 digit TRUE vampires.

A number v = xy with an even number (n) of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y together is known as vampire number. Pairs of trailing zeros (Both the numbers have a trailing zero) are not allowed. If v is a vampire number then x and y are called its "fangs." Examples of 4-digit vampire numbers include

1. 21 x 60 = 1260
2. 15 x 93 = 1395
3. 35 x 41 = 1435
4. 30 x 51 = 1530
5. 21 x 87 = 1827
6. 27 x 81 = 2187
7. 80 x 86 = 6880

Vampire number counts
 Digits Vampireratio Vampires with at least f different fang pairs Vampireequations Primevampires f=1(all vampires) f=2 f=3 f=4 f=5 4 1/1286 7 0 0 0 0 7 0 6 1/6081 148 1 0 0 0 149 5 8 1/27881 3228 14 1 0 0 3243 57 10 1/82984 108454 172 0 0 0 108626 970 12 1/204980 4390670 2998 13 0 0 4393681 26653 14 1/431813 208423682 72630 140 3 1 208496456 923920

Vampire ratio is (n-digit vampire numbers)/(n-digit integers) and not a ratio of performed tests.
Vampire equations are all equations of the form vampire = fang1 · fang2, i.e. each vampire number counts for each different fang pair. Prime vampires obviously only have one fang pair.
The vampire equations for all table counts below 15 are on this page.

First 15 vampires with exactly 2 fang pairs
 125460 = 204 · 615 = 246 · 510 11930170 = 1301 · 9170 = 1310 · 9107 12054060 = 2004 · 6015 = 2406 · 5010 12417993 = 1317 · 9429 = 1347 · 9219 12600324 = 2031 · 6204 = 3102 · 4062 12827650 = 1826 · 7025 = 2075 · 6182 13002462 = 2031 · 6402 = 3201 · 4062 22569480 = 2649 · 8520 = 4260 · 5298 23287176 = 2673 · 8712 = 3267 · 7128 26198073 = 2673 · 9801 = 3267 · 8019 26373600 = 3600 · 7326 = 3663 · 7200 26839800 = 2886 · 9300 = 3900 · 6882 46847920 = 4760 · 9842 = 6290 · 7448 61360780 = 7130 · 8606 = 7613 · 8060 1001795850 = 10170 · 98505 = 19701 · 50850

"Then give to the world the best you have, And the best will come back to you."

Damn Catch33;

Now I have been away for awhile here and just popped back in to see what is all the commotion is going on here........ I see that you have been staying up a little to late in the lab of yours, and then there was a explosion here..... but the info that you had written out was written in one of those major scientific writings!

Nevertheless...... when you break it down........ we all will still be here for the layman's booklet.

Have a great day my friend!

Maverick2842........ out.

Thank you and have a prosperous day!

Maverick2842.......out!

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